(Sample) 3rd order Multiple Feedback Low-pass Filter Design Tool - Result -

Calculated the Transfer Function for the 3rd order Multiple Feedback Low-pass filter, displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response.

3rd order Multiple Feedback Filter

Vi→

→Vo

(Sample)Transfer Function:

G(s)=

-79063161.7478

s³+466.724312356s²+392148.494742s+80593959.1348

R1 = 910Ω
R2 = 47kΩ
R3 = 130kΩ
R4 = 47kΩ
C1 = 4.7uF
C2 = 0.22uF
C3 = 0.0022uF

Equivalent block diagram:

Vi(s)→

2πfc1

s+2πfc1

→

(2πfc2)²

s²+2ζ(2πfc2)s+(2πfc2)²

→Vo(s)

Cut-off frequency fc1, fc2 of equivalent block diagram:

fc1 = 37.9811225476[Hz]
fc2 = 92.4905889032[Hz]

Damping ratio ζ of equivalent block diagram:

ζ = 0.196238121389

Pole(s)

p = -18.1501794125 +90.6922269158i[Hz]
  |p|= 92.4905889032[Hz]
p = -37.9811225476[Hz]
  |p|= 37.9811225476[Hz]
p = -18.1501794125-90.6922269158i[Hz]
  |p|= 92.4905889032[Hz]

Phase margin

pm= 214[deg] (f =89[Hz])

Oscillation frequency

f = 90.6922269158[Hz]

Overshoot (in absolute value)

The 1st peak  g_pk = -1.01 (t =0.0085[sec])
The 2nd peak  g_pk = -0.85 (t =0.013[sec])
The 3rd peak  g_pk = -1.02 (t =0.019[sec])

Final value of the step response (on the condition that the system converged when t goes to infinity)

g(∞) = -0.981006053016